Imprint. Why Lewis s analysis of modality succeeds in its reductive ambitions. Ross P. Cameron. Philosophers. University of Leeds

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1 Imprint Philosophers volume 12, no. 8 march 2012 Why Lewis s analysis of modality succeeds in its reductive ambitions. Ross P. Cameron University of Leeds 2012 Ross P. Cameron This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. < 1. Lewisian Modal Realism Many have felt the attractions of a reduction of the modal to the non-modal. There s something unattractive about the claim that the world just could have been otherwise and that that s the end of the matter nothing more illuminating to say! Such a primitivism about modality threatens to leave the notion mysterious, and the primitivist leaves themselves open to the challenge from the sceptic that their notion is not in good standing. Of course, there are intermediate options between ending the story where the simple primitivist ends it and offering a fully reductive account of the modal and I will have more to say later about just why a thorough reduction of the modal is desirable but it is at least evident that the prospects for reduction are of interest. The most well worked out attempt at a reduction of the modal to the non-modal remains David Lewis s Modal Realism. 1 I say attempt at a reduction, not because I think it fails as a reduction, but because others have made the claim that it does. It will be the aim of this paper to argue that it does not fail: that Lewisian Realism is a genuine and successful, completely reductive account of modality. Along the way I hope to shed some light on what a reductive analysis of modality and, indeed, analyses in general need to accomplish to be successful, and why reduction is desirable. Lewis s starting point are the Leibnizian biconditionals: p is necessary iff it is true at every possible world, possible iff it is true at some possible world, and actually true iff it is true at the actual world. If these biconditionals are true, then to provide a reduction of the modal to the non-modal, one need only provide non-modal analyses of the notion of a possible world, actuality, and what it is to be true at a world. Lewis makes two assumptions in his definition of a possible world. The first is unrestricted mereological composition: for any collection of objects, the Xs, there is an object which is the sum of the Xs. The second is that there is a dyadic equivalence relation x is spatiotemporally, or analogously, related to y. That is, we can take all the things that 1. The canonical source being, of course, Lewis (1986).

2 there are and divide them into groups such that every thing is in exactly one group, each member of a group bears some spatiotemporal relation (like is 4 meters from, or is 2 years from) to each other member of that group, or at least bears some relation analogous to a spatiotemporal relation, 2 and no two members of distinct groups stand in any spatiotemporal relation. A possible world, then, is an object whose parts are all and only the members of one of these groups. That is, it is a mereological sum each of whose parts is spatiotemporally related to each of its other parts, and is such that nothing that is spatiotemporally related to any of its parts fails to be a part of it. And this is merely a matter of definition. Think of this as introducing a new semantically simple term possible world into the language. The fact that the string of letters possible appears here is no more significant than the fact that the string ham appears in hamburger : to conclude from the former that Lewis s notion of a possible world is modal would be as much a mistake as when people assume that hamburgers are made from ham. If there is modality in Lewis s account of what a possible world is, it must be because some of the notions we appealed to in defining such things involve modality, such as the mereological notions, or the concept of a spatiotemporal relation. Whether this is so is something we shall come back to. Next, we need an account of what it is to be true at a world. According to Lewis, working out what s true at a world is just a matter of restricting one s attention to the portion of reality as a whole that is that world. There s nothing special about modality here: we do the same thing as we would if we wanted to know whether something is, e. g., true in Scotland. Suppose, for example, I am interested in discovering whether Everyone likes Scotch is true in Scotland. Here s a bad way to answer me. You point to the existence of someone in England who doesn t like Scotch, thereby showing that not everyone likes Scotch; you then argue that propositions aren t true relative to places, and hence that my question is either confused, because it presupposes that 2. I ll drop the qualification henceforth. they are, or that it should be answered in the negative that is, that Everyone likes Scotch is false in Scotland because it is false simpliciter, and the in Scotland isn t doing any work, since propositions aren t true relative to places. That would be a bad way to answer my query: there is obviously sense to be made of the question Is it true in Scotland that everyone like Scotch?, and the existence of someone in England who doesn t like Scotch is irrelevant to answering this question. What the question is asking us to do is to restrict our attention to a portion of reality the Scottish portion to restrict the domain of our quantifier to people in Scotland, ignoring those in England and elsewhere, and to ask, with our quantifier so restricted, is Everyone likes Scotch true? The existence of the aesthetically challenged Englishman is obviously irrelevant to this question, for he is not in the domain of the quantifier, so restricted. And so it goes with worlds. When we ask whether Everything is red is true at a world w we are, says Lewis, asking about the truth of the sentence with the domain of the quantifier restricted to those things which are parts of the world w. The claim is true at w iff all the parts of w are red; the existence of non-red things that are not a part of w is utterly irrelevant. Now, that only tells us how to assess some claims with our attention restricted to a world. It s obvious how to assess Everything is F or The G is H with respect to a portion of reality: we just look to see whether everything that is a part of that portion of reality is F, or whether the G that is a part of that portion is H. It s less obvious what to do with, e. g., It s morally wrong to eat apples. I presume this is false. But could it be true? Is it true at some world? It s not obvious how to tell. How do I assess that claim with respect to some portion of reality? Of course, on certain views of morality this wouldn t be hard to answer. If a strong naturalism is true, and moral facts supervene on the instantiation of natural properties by ordinary entities in spacetime, then presumably we can assess a moral claim with respect to a portion of reality by looking at what natural properties are instantiated by the entities that are parts of that portion. But we shouldn t have to rely on such an account of morality being true in order to accept modal realism: we should philosophers imprint 2 vol. 12, no. 8 (march 2012)

3 have something to say about how to assess moral claims for truth with respect to a portion of reality even if moral truths are sui generis and non-natural. But it s not clear how to do this: if moral facts don t simply amount to facts about the natural properties of the inhabitants of worlds, how does restricting our attention to some such inhabitants impact on how we should assess a moral claim? 3 The worry would be that any account here is going to have to involve modality: that the claim is true with respect to some portion of reality iff it would be true (simpliciter) were that portion of reality all that existed. But really, I think this worry is a red herring. I think that what Lewis should say is that for some claims, restricting our attention to a portion of reality simply makes no difference. For those claims, whether or not they are true at some portion of reality a fortiori whether or not they are true at a world will simply be a case of whether or not they are true simpliciter. 4 In that case, there is no room for contingency with respect to such claims: whatever their truth-value simpliciter, this will be their truth value at every world (and hence they will be either necessary, if true, or impossible, if false), since restricting one s attention to a world can never make a difference. 5 Now, 3. Other potentially recalcitrant claims include: claims about the laws of nature, given a primitivist view on laws, or a view on which laws are relations amongst transcendent (Platonic) universals; claims about non-spatiotemporal entities like sets and numbers (see fn. 5); logical truths, such as what is a theorem or what follows from what; etc. The common theme is that these truths do not appear to be about, or made true by, spatiotemporal entities; so it s hard to see what restricting your attention to some spatiotemporal entities rather than others does when assessing them for truth. 4. One is reminded here of Fine s (2005) distinction between those truths which would be true no matter how the world was, and those which are true irrespective of how the world is. 5. Lewis on sets can be seen as a particular instance of this. Since pure sets, at least, are not, presumably, spatiotemporal, and a fortiori not spatiotemporally related to anything, they are by definition not a part of any world. Nonetheless, thinks Lewis, we can make sense of the claim that pure sets exist at a world: while they are not parts of any world, they can exist from the standpoint of a world, where an entity exists from the standpoint of a world iff it belongs to the least restricted domain that is normally appropriate in evaluating the you might think this is an objection to Lewis: that any account of modality should allow for the contingency of, e. g., moral claims, even given a sui generis non-naturalism about morality. Maybe it is so; I take no stand on that here. All that s important for present purposes is that assessing a claim for truth at a world is a non-modal business according to the Lewisian. For the truths where it makes a difference, it s a simple matter of assessment with respect to a restricted domain; for the truths where is doesn t make a difference, it s simply a matter of assessing for truth simpliciter. So we have a story of what worlds are, and a story of what s true at a world, and there is no obvious modality at play in either story. The final piece of Lewis s story is the account of actuality: the actual world is defined as the world that has me as a part. Not that there s anything special about me: everyone can truly say, The actual world is the world that has me as a part. Actual, says Lewis, is an indexical like here or now : it serves to pick out the world of the utterer the unique world that has them as a part just like here and now serve to pick out the spatial or temporal location of the utterer. So two people in two distinct worlds can make different claims about what is actual without there being genuine disagreement, in the same way speakers at different spatial/temporal locations can make different claims about what s going on here/now without there being any genuine disagreement. So actuality is just me and my spatiotemporal surroundings: again, no obvious modality here. truth at that world of quantifications (Lewis [1983], p. 40). Lewis doesn t have too much to say about how we tell what restrictions are normally appropriate at a world other than that freeing up the quantifier so that we can truly say that there s a plurality of worlds is deemed abnormal but it seems likely that whether or not pure sets are in the domain of the least restricted domain that is normally appropriate for evaluating quantifications is not something that is going to vary from world to world. Why would it? Why would the presence of talking donkeys, e. g., affect whether or not I can truly say The null set exists when I m speaking as unrestrictedly as I can do without forcing an abnormal context? In that case, it simply falls out that the pure sets are necessary existents, since restricting your attention to a world can never make a difference. And on the assumption that numbers are pure sets, it will also fall out that the truths of mathematics are necessary truths. philosophers imprint 3 vol. 12, no. 8 (march 2012)

4 Lewis s account of actuality demands that objects are world bound: they are parts of only one world. 6 For, obviously, if I existed at multiple worlds, I would not succeed in my definition of the actual world as the world that has me as a part, for there would be a false presupposition. 7 This demands a wrinkle in the above account of what is true at a world. For modality de dicto, the above account is fine. But when we re concerned with modality de re when I want to know whether I might have been a tree, e. g. the account must be complicated. For if I restrict my attention to the things that are parts of some non-actual world w and ask whether Ross is a tree is true with my attention so restricted, the answer will always come back, on the unmodified account, that it is not true, because I will never be amongst the things I have restricted my attention to, because I am a part of the actual world only. And so the unmodified account tells us that a predication of me is only true at one world, the actual world; hence, no false predication of me is true at any world whatsoever, and hence we are threatened with the extreme essentialist view that everything actually true of me (and likewise, mutatis mutandis, for any thing whatsoever) is not possibly false of me. In order to avoid this extreme essentialism, Lewis says that for a de re claim to be true at a world w requires not that the res itself be a part of w and be the way the claim says it is, but rather 6. More precisely, it demands that objects which are parts of any world are parts of exactly one world. Given unrestricted composition, Lewis is committed to objects which have as parts objects which exist at different worlds; but these objects don t exist at any world: there is no world which has them as a part. The existence of such objects doesn t threaten the definition of actuality : only objects which are parts of more than one world would do that. 7. According to the endurantist, I exist at more than one time. If it is so, now can t serve to pick out the temporal location of the utterer, for they have no unique temporal location. But here there is an easy fix: now serves to pick out the temporal location of the utterance. But this won t help in the modal case: we can t say that utterances but not utterers have a unique modal location, and define the actual world as the unique world that has my utterance I am actual as a part. For if the utterer belongs to some non-actual world v then the utterance, by virtue of being spatio-temporally related to the utterer (which it must be if it is to be actual), is also spatio-temporally related to v, and hence, by the definition of world, is a part of v contrary to our assumption that it is world-bound. that there is a counterpart of the res at w that is the way the de re claim says w is. So, e. g., if I want to know whether Ross is a tree is true at w, I look to the parts of w and ask whether any of them are both a tree and my counterpart: the claim is true at w iff there is such a part. What is a counterpart of me? An object is my counterpart iff it is saliently similar to me, where the standards of similarity that are salient depends on the context. Again, no obvious modality anywhere in this story. So the resources Lewis needs to get his attempted reduction of modality going are: (i) Unrestricted composition, to ensure the existence of the worlds. 8 (ii) The existence of an equivalence relation is spatiotemporally related to, to specify which of all the mereological sums that there are, are the worlds Two caveats. Obviously, full unrestricted composition isn t necessary to ensure the existence of the worlds. One could, for example, hold that composition only ever occurs amongst worldmates. Secondly, it s not obviously bad for Lewis s analysis if there simply are no worlds. The work done by talk of worlds is in separating reality as a whole into different possible circumstances; but all one needs in order to be able to say whether some objects or events, etc., belong to the same possible circumstance is to be able to say whether or not they are worldmates, and one doesn t need there to be worlds in order to say whether some things are worldmates: they are worldmates iff they are spatiotemporally related. So instead of saying that there are worlds, we could rather introduce a plural predicate: The Xs world is stipulated to mean that the Xs are worldmates, and that nothing is a worldmate of any of the Xs that is not one of the Xs. We would then replace talk of p s being true at a world w with talk of p s being true at some Xs which world. This doesn t pose any obvious problems for Lewis s account of true at in terms of restricting our attention to a portion of reality: we re merely restricting our attention to some things and asking what s true at them rather than to some thing and asking what s true at it. And so perhaps Lewis can refrain from even making any assumptions about mereology; but I will deal with the theory as Lewis gives it to us, and assume unrestricted composition. 9. Perhaps a Lewisian realist could cope with is spatiotemporally related to failing to be an equivalence relation by tweaking the definition of world. I won t worry about this here: of all the things you might object to about Lewisian realism, that it assumes that is spatiotemporally related to is transitive is not high on the list. philosophers imprint 4 vol. 12, no. 8 (march 2012)

5 (iii) The account of evaluating a de dicto claim once our quantifiers are restricted to a portion of reality, to say when a de dicto claim is true at a world. (iv) The notion of a standard of similarity s being contextually salient, in order to say what a thing s counterparts are, and hence to say when a de re claim is true at a world. There are two ways, then, in which we might argue that Lewis doesn t succeed in giving a thorough reduction of the modal to the non-modal. Firstly, we might argue that he is wrong to think the above resources sufficient, and try to show that the extra resources needed involve modality. Secondly, we might argue that, despite appearances, modality is involved in the above resources. I will take these in turn. 2. The Lycan/Shalkowski objection Various people have made an attempt at arguing that for Lewis s account of modality to succeed, he needs resources beyond those mentioned above, and that such resources must be modal for the account to work. If so, Lewis s reductive ambitions must fail. I think this is not so, but it is instructive to see why. I will begin by looking at a familiar charge against Lewis: that his notion of a possible world must be modal if his theory is to give the correct results. This charge has been made by William Lycan and Scott Shalkowski. Lycan says: 10 Lewis mobilizes a modal primitive. It is world. World for him has to mean possible world, since the very fleshand-bloodiness [of worlds and non-actual individuals] prevents him from admitting impossibilia. Some sets of sentences describe worlds and some (the inconsistent ones as we know them to be) do not; but Lewis cannot make that distinction in any definite way without dragging in some modal primitive or other. 10. Lycan (1988), p. 46). And here is Shalkowski: 11 According to modal realism, the existence of a group of objects, the possible worlds, is supposed to be the foundation for modal truths. The existence and natures of these worlds is the primitive feature of modal reality, while the necessitites and possibilities are parasitic on the nature of the set of worlds. For this account to work, there can be no modal restrictions on these worlds. Possible worlds must constrain facts of modality; facts of modality must not restrict the number and nature of possible worlds. Were God creating the entire Lewisian plurality of worlds, there would be no modal restriction on God s act of creation. To say that God had no choice as to which or how many worlds to create is to say that there are modal constraints on the number and nature of possible worlds, and this is tacitly to give up the reductive features of the modal realist s program. [O]ne constraint on any reductive theory of modality is that all objects in the reductive base, those things whose existence and nonmodal attributes are to ground modality, must be objects that possibly exist [A]ll the objects [must] meet the prior modal condition that they are possible. [p. 677; original italics] For the set of nonactual objects to be sufficient for grounding modality it must meet a second modal condition. The set must be exhaustive, and it is exhaustive only if it cannot have any more members. The modal realist s claim that there are no more worlds is irrelevant apart from the claim that there cannot be any more. If 11. Shalkowski (1994), p philosophers imprint 5 vol. 12, no. 8 (march 2012)

6 there could be more but just aren t, the set is inappropriately small. [p. 675] Actually, I think there are two distinct objections being run together in Shalkowski s paper. One of them is the same as, or at least very similar to, Lycan s; the other is easier to dispense with, so we ll deal with that first. Shalkowski says For [Lewis s] account to work, there can be no modal restrictions on these worlds. [F]acts of modality must not restrict the number and nature of possible worlds. Were God creating the entire Lewisian plurality of worlds, there would be no modal restriction on God s act of creation. 12 It seems that Shalkowski is worried here about modal facts concerning the space of possible worlds as a whole. For Lewis, what s possible for a world is given by how its companion worlds are. But what about what s possible for reality as a whole that is, all the worlds? Lewis says that the facts about the worlds as a whole are a non-contingent matter; 13 I take it that Shalkowski s worry is that if this is so, there s no explanation for where the modal restrictions are coming from. Here is a modal restriction on the space of worlds, but the space of worlds was meant to be what yielded any modal restrictions. This objection can be easily set aside. It s not that there can t be any modal restrictions on the nature or number of worlds for Lewis s account to work; it s that any such modal restrictions must themselves be amenable to the Lewisian analysis. All modality must be amenable to the Lewisian analysis for the analysis to provide a thorough reduction of the modal, a fortiori any modal facts about the space of worlds themselves must be so amenable. And no modal facts count against the analysis if they are amenable to the analysis itself, a fortiori it is no objection to the analysis if there are modal restrictions on the number or nature of worlds, provided those modal facts are themselves 12. Ibid. 13. E. g. Lewis (1986), p amenable to analysis in the Lewisian manner. It would indeed be a damning objection to Lewis were there modal facts about the number or nature of worlds which proved resistant to the proposed analysis; that s because it would be damning were there any modal facts, regardless of subject matter, that proved resistant to the analysis, since the analysis is meant to be a general account of what modality is. But the mere obtaining of such modal facts is neither here nor there, and Shalkowski gives us no reason to suppose that such facts are themselves resistant to the Lewisian analysis. Here s how the Lewisian should deal with modal facts about the space of worlds themselves: claims about the space of worlds as a whole are amongst the claims such that restricting your attention to a portion of reality cannot make a difference in how you assess them for truth or falsity. Hence, as with all such claims, claims about the space of worlds as a whole are simply necessary, if true, or impossible, if false. 14 If you re assessing There are pigeons for truth at a world, you re restricting your attention to some things and asking whether pigeons are amongst them: the answer depends on which things it is you re restricting your attention to, and it is in virtue of that that There are pigeons is contingent. But when it comes to claims about the space of worlds as a whole such as that there is a plurality of worlds restricting one s attention simply makes no difference. For Lewis, when we re asking about what is the case, we re asking most of the time about what is the case at some small portion of reality in which case, of course it often matters which portion of reality we re concerned with. And that s what contingency is, says Lewis: variation from one portion of reality to another. But of course how reality is as a whole doesn t vary from one portion of reality to another! 15 That s why 14. See footnotes 3 and 5, and the corresponding discussion in the text. What I say here is, I think, broadly consonant with the treatment developed by Divers (1999). 15. Compare: Whether There is beer is true or false depends on whether I am restricting my attention to the contents of my fridge or including the contents of the grocery store; but whether There is unrestrictedly beer is true or false philosophers imprint 6 vol. 12, no. 8 (march 2012)

7 Lewis s account of modality simply doesn t allow for contingency in such claims: they are necessary if true, and impossible if false. So the modal facts about the space of possible worlds are perfectly amenable to the Lewisian analysis. Such modal truths pose no threat to Lewis s reductive ambitions, and so Shalkowski s first objection is unmoving. I propose then to move swiftly on to the common objection from Lycan and Shalkowski. Here s the objection, as I see it. I said above that the occurrence of possible in the phrase possible world, as Lewis uses it, is no more significant than the occurrence of rat in Socrates : as far as Lewis s theory goes, we might as well call those big individuals squanks, and say that something is possible iff it s true at some squank. The Lycan/ Shalkowski objection is basically that if that is so, then nothing guarantees that Lewis s account is even materially adequate. Who knows whether the facts about squanks match up in the appropriate manner with facts about what could be the case? We have no reason to believe there is such a correspondence: unless, of course, our understanding of squanks is implicitly modal, so that their nature compels the facts about them to match up with the facts about what s possible. The material adequacy of Lewis s proposed analysis demands both that there is a world corresponding to every possibility, without exception, and that there are no worlds corresponding to any impossibility. But if the notion of a world is not modal, what can ensure this? Nothing, they claim. To guarantee that there is the required correspondence between what s possible and what s happening at some world, argue Lycan and Shalkowski, we need the notion of a world to be a modal one. These worlds must be possible worlds, where this isn t just a matter of labeling, but rather makes appeal to our prior modal notions. Only once you use a modal notion to characterize the nature of these things do we have a guarantee that the facts about them correspond in the right way to the modal facts to make the Leibnizian biconditionals come out true. But, of course, if we need to use a modal notion to does not so vary. Restricting one s attention makes no difference to the domain of the unrestricted quantifier. characterize the nature of worlds, then world is not a non-modal notion, and hence we lack a fully reductive account of modality. I think this objection is mistaken and relies on a misunderstanding of the nature of analysis. Suspicion should be raised by the fact that, if the objection is successful, it s hard to see how any reductive analysis could be possible. Consider a proposed reductive analysis of the Φ-facts in terms of the Ψ-facts. A condition of success is that the analysis be materially adequate: there had better be the right kind of correspondence between the Φ-facts and the Ψ-facts. But unless our concept of Ψ implicitly involves an appeal to the concept of Φ, what can ensure this? But of course, if our concept of Ψ does so involve the concept of Φ, the reduction must fail. That can t be right. What goes wrong? I think talk of ensuring that an analysis is materially adequate is misleading. In one sense, it s trivial that that the analysis is ensured to be materially adequate. After all, if the analysis of the Φ-facts in terms of the Ψ-facts is indeed correct, then there is no question of the Ψ-facts not corresponding in the appropriate manner (i. e. to ensure material adequacy) to the Φ-facts precisely because, if the analysis is correct, the Φ-facts simply are the Ψ-facts! I think that simple reply is broadly correct. So Lewis should simply reply to Lycan and Shalkowski as follows: What ensures that the worlds correspond in the right way to the possibilities is my analysis of possibility. There is no question of there being a world corresponding to an impossibility, because my analysis says that what it is to be possible is to be true at some world, so of course whatever worlds there are correspond to possibilities, and no world corresponds to an impossibility. (Similarly, there is no question of any world containing an impossible individual, since my analysis tells you that to be a possible individual just is to exist at some world.) I need no prior modal constraints on the nature of worlds to ensure this: what I mean by possible ensures this. Similarly, there philosophers imprint 7 vol. 12, no. 8 (march 2012)

8 is no question of there not being enough worlds i. e., that some possible circumstance be unrepresented by a world. Given what my analysis says possibility is, it simply follows that whatever the extent of the space of worlds happens to be, that is the extent of what is possible. Again, no prior constraints on the nature of worlds is necessary to ensure that there is a world for every possibility: this is guaranteed by what I mean by possibility. So Lycan asks: How can you, Lewis, avoid admitting impossibilia? Don t you need world to mean possible world or individual to mean possible individual 16 to ensure that this be the case? Lewis should reply: No, I don t need a modal understanding of world or individual. I can guarantee that there are no impossibilia because if they exist, my analysis says precisely that they re not impossibilia they re possibilia! If Lewis s analysis is right, then if there turns out to be a world with a round square as a part, then that is not for it to turn out that there is an impossible world; it s for it to turn out that round squares are in fact possible after all, since to be possible just is to be true at some world, if the analysis is correct. Likewise, Shalkowski asks how Lewis can guarantee there s a world for every possibility. Answer: because if Lewis s analysis is right, then if there turns out to be no world with a talking donkey as a part, e. g., then that is not for it to turn out that there is a possible world missing; it s for it to turn out that talking donkeys are not in fact possible after all, since to be possible just is to be true at some world, if the analysis is correct. There s simply no challenge to Lewis when it comes to ensuring that there are worlds enough for the possibilities, or ensuring that the worlds are not too many to 16. This latter challenge is the gist of Lycan (1991). In reply to Miller s (1989) claim that Lewis has a non-modal definition of world available, Lycan argues that this is not so, because the definition talks about sums of worldmates, and in order to ensure that round squares don t end up as parts of worlds our notion of the individuals that are worldmates must be implicitly modal: they are the possible individuals. encompass impossibilities: since the space of possibilities is given by the space of worlds, it s simply trivial that if the analysis is correct then there are exactly worlds enough for possibility. Here s a bad response to this defence of Lewis: You ve said the analysis itself ensures that the worlds match up to possibilities in the required manner. That if there are worlds with, e. g., round squares, then if the analysis is correct, that just means that round squares are possible, and so it is a trivial matter to ensure that impossibilia are excluded from ontology. But whether the analysis is correct is what s up for debate you can t rely on the analysis without begging the question! That s a bad response. If someone is trying to show that your theory doesn t work, you re perfectly entitled to rely on your theory in arguing that those objections don t succeed. Lycan and Shalkowski are the ones putting forward the argument against Lewis. It s up to them to show that his theory is false, and Lewis can appeal to any of his beliefs in resisting their argument. Just because his objectors don t also believe what he relies on when making his defence doesn t mean he begs the question: it just means he disagrees with them. Now, there s something else one might be after if asking for a guarantee that the analysis is materially adequate. We could be asking for a guarantee that the facts about what s true at a world match up, more or less, with what we pre-theoretically take to be the facts about what s possible. Here s the idea. I said that Lewis can respond to Lycan s request for a guarantee that his (Lewis s) ontology contain no impossibilia by pointing out that according to his analysis of modality, whatever happens to exist is possible. Lewis doesn t need an understanding of world that will rule out worlds having round squares as parts: if there is a world with a round square as a part then that, according to the analysis, just means that round squares are possible. But one might object that we simply know that round squares are not possible. So Lewis really does need to ensure that no world has a round square as a part, because otherwise his analysis would incorrectly yield the conclusion that there could be round squares. philosophers imprint 8 vol. 12, no. 8 (march 2012)

9 Here s an analogy. Consider the consequentialist analysis of goodness in terms of best outcome. The consequentialist says that there is an ordering of possible histories from best to worst, and that the good actions for person P to perform in a particular set of circumstances C are those actions that P can perform in C whose consequences lead to no worse a history than that of any other possible action P could perform in C. Obviously, the consequentialist account of goodness is acceptable if and only if the facts about what s good correspond in the appropriate way with the facts concerning the betterness ordering of the consequences of possible actions. A well known style of objection to consequentialism argues that this is not the case: no matter how good the consequences, says the objector, torturing babies for fun, e. g., is just wrong! Now, here s one way of taking that objection: Torturing babies for fun is wrong. The consequentialist says that an action is wrong only if there s another possible action that would have better consequences. So for their account to be materially adequate, they had better ensure that there s something we can do other than torturing babies for fun that would have better consequences. But the only way to ensure this is if the way consequences are ordered from better to worse meets the prior moral condition that histories where babies are tortured for fun are worse than ones in which they are not. It would be a damning objection to consequentialism if the notion of betterness they use to order consequences of actions implicitly involved the notion of goodness that they are attempting to analyse. But the consequentialist should not be moved at all by this objection. She doesn t believe there are prior moral conditions to be met: the moral facts are, she thinks, given by the ordering of consequences of possible actions from better to worse. If the consequences of torturing this baby for fun really are better than the consequences of not doing so then, says the consequentialist, that s not for it to turn out that a wrong action has the best consequences; it s for it to turn out that it s not the wrong thing to do after all. However, here s another way of taking the objection that may move the consequentialist more: We just know that torturing babies for fun is wrong. If an account of goodness tells us that torturing babies for fun can be the good thing to do then that s just a reductio of the account. So you d better ensure that there s always something we can do other than torturing babies for fun that would have better consequences, if you want your account of goodness to be acceptable. The two objections are crucially different. The first aims to embarrass the consequentialist into admitting that they haven t provided a reductive account of goodness, because they need to appeal to that very notion when ordering the consequences of actions from better to worse. The objection challenges the consequentialist s reductive ambitions. This objection is easily resisted. The second objection does not aim to show that the notion of better than used in the ordering of consequences from better to worse must implicitly involve the notion of goodness that was to be analysed. Rather, the second objection says that for the account of goodness to be warranted in the first place, the ordering of consequences must respect certain of our pre-theoretic beliefs about what is good. The thought behind the second objection is simply this. Analyses can be to some extent revisionary. Perhaps we pre-theoretically think that infanticide is always wrong; but it s open that we can learn from a successful moral analysis that there are circumstances in which it s permissible. But an analysis can t overturn everything we thought to be true about the facts to be analysed. If a proposed analysis of goodness told us that murder was always permissible, giving to charity always forbidden, torturing babies supererogatory, etc., etc. well, we philosophers imprint 9 vol. 12, no. 8 (march 2012)

10 just shouldn t think that what that analysis is talking about is what we mean by goodness. A certain amount of coherence with our pretheoretic beliefs about the phenomenon to be analysed is necessary in order for us to accept the account as an analysis of that phenomenon, rather than as simply having changed the subject. I said that Lewis should respond to Lycan and Shalkowski thus: that if it turns out that there are worlds with round squares as parts, that s just for it to turn out that round squares are possible after all; if it turns out that there s only one world, our own, that s just for it to turn out that everything is necessary after all. It s not for it to turn out that there are impossible worlds, or not worlds enough for possibility, respectively. I think that response is right, but one might still complain as follows: But we just know that round squares are not possible and that more is possible than what is actual, so Lewis can t simply end the story here. He needs to be able to account for these pre-theoretic data about possibility by ensuring that there are no worlds with round squares as parts, and that there s more than one world, in order for us to think that what s being analysed is really possibility. If Lewis is leaving it open that there s only one world, or that there are worlds containing round squares, then while I accept that if his analysis is right this wouldn t lead to a mismatch between modal facts and facts about worlds, it undermines my warrant for thinking that the analysis is right in the first place. There s definitely something right about that. An analysis can be informative, but it can t be drastically revisionary, so what s true at a world had better not come too far apart from what we pre-theoretically think is possible if Lewis s analysis is to be acceptable in the first place. But crucially, it need be no part of the analysis itself that the facts about what s possible according to the analysis match up more of less with our pretheoretic conception of those facts. An account of what possibility is, is one thing; an account of what is in fact possible, another; and these two things shouldn t be confused. Lewis owes a story about the extent of worlds, certainly; and the resulting account of what is possible had better not be too revisionary with respect to our pre-theoretic modal beliefs; but there should be no demand that this story about the extent of worlds fall out from the analysis that it be entailed by the meaning of world or the nature of worlds. That would be to confuse the two things that should be kept separate. So Lewis s analysis of what possibility is needn t ensure that there is the right kind of correspondence between what worlds there are and what we pre-theoretically take to be possible. There simply needs to be such a correspondence (or perhaps: we simply need to have a warranted belief in there being such a correspondence in order for us to have warrant for the analysis); it need not be guaranteed by the nature of the worlds or the definition of world that there is such a correspondence (and so our warrant for belief in such a correspondence needn t come solely from the analysis). After all, it s not a conceptual truth that it s not possible that there are round squares, or that something other than what is actual is possible. Dialetheists like Graham Priest believe that some contradictory states of affairs are possible; 17 Spinoza thought that everything that was true was necessarily true. 18 I think they re wrong, but I don t want to claim that they re conceptually confused or employing a concept other than our concept of possibility! They are using the same modal concepts we are, and they are competent graspers of the concept and users of the term possible ; they just have radical views about the extent of what is possible. Compare again the case of the consequentialist. Of course the consequentialist can, and many do, simply bite the bullet and claim that there are possible circumstances in which it s good to torture babies for fun. Perhaps their account of goodness can survive this, perhaps not. For present purposes, I am interested in what the consequentialist 17. See inter alia Priest (1987). 18. At least, this is a common and plausible interpretation of Spinoza. See Newlands (2010) for discussion. philosophers imprint 10 vol. 12, no. 8 (march 2012)

11 can do if she wants to hang on to the claim that it is always and forever wrong to torture babies for fun. She ll need to claim that there s always going to be something we can do that will have better consequences than torturing babies for fun. So when we order with respect to betterness the histories that would obtain if each of the possible actions open to us were taken, a baby-torturing history had better never come out (tied for) best. But it need be no part of the concept of better, or the nature of betterness, that this is so: it only need be so. Or perhaps, for consequentialism to be acceptable, we need to be able to gain warrant that it is so. But again, this warrant needn t come from the consequentialist analysis of goodness, since it need be no part of the analysis of goodness that torturing babies for fun is never the good thing to do. The account of what goodness is, is one thing; the account of what is in fact good, another. Here s a toy example of how the consequentialist could achieve the desired results. Take betterness to simply be most happiness, and suppose that God will punish people who torture babies for fun with infinite unhappiness in Hell, and that every other action will lead only to some finite level of happiness or unhappiness. If that s correct, then any history without a baby being tortured for fun is better than any history with. Now, I m not recommending that the consequentialist believe this; the point is just that if the consequentialist wished to hang on to the pre-theoretical moral claim that it s never okay to torture babies for fun, this would be a way to do it. And it s clear that this theory does not smuggle the concept of goodness into the concept of betterness as applied to consequences of actions: the latter concept is cashed out solely in terms of maximizing happiness. The theory is, of course, designed precisely to ensure that the facts about betterness match our pre-theoretic beliefs concerning the facts about goodness. But it s not the consequentialist analysis itself that guarantees this match. As far as the analysis of goodness in terms of having best consequences (i. e., the consequences that maximize happiness, on this account), it s simply an open question whether or not torturing babies for fun can ever be good. It s something else the consequentialist believes something not entailed by the analysis that closes this question, in a way that shows that this consequentialist is not revisionary with respect to this tenet of folk morality. And this is okay: the analysis of goodness is one thing; the extent of what is good, another thing entirely. There is no need for this question about the extent of what s good to be settled by the analysis itself. Likewise, the analysis of possibility is one thing, and the extent of what is possible, another. Since it s no part of the concept of modality that round squares are impossible and talking donkeys possible, Lewis doesn t need it to fall out from the definition of world, or from the nature of worlds, that there is no world with a round square as a part or that there is a world with a talking donkey as a part. However, since it is true that round squares are impossible and talking donkeys possible (so I believe, at least), it must be true that there are no worlds with round squares as parts and that there are worlds with talking donkeys as parts. And, indeed, Lewis says that it is true. It doesn t follow from the nature of worlds, or from the definition of world, that the extent of the worlds is so but so what? It needn t do so, since it is no part of the analysis of modality that the extent of possibility is so. All that need be the case is that the space of worlds is in fact so, since all that is the case is that the extent of modality is in fact so. And what is the reason for thinking that the space of worlds is so? Why should we believe Lewis that there is a world with a talking donkey as a part, and no world with a round square as a part? Because of the theoretical utility such an ontological posit affords part of which, of course, is that it allows for a reduction of the modal. Now of course, you could question the methodology here you might think that theoretical utility is not a good reason to accept metaphysical theses but it s clear that that would be a very different style of objection from the Lycan/Shalkowski objection, and would be nothing to do with Lewis s appealing to hidden primitive modality. 3. The Divers/Melia objection So I think the Lycan/Shalkowski objection poses no threat to Lewis. I want to now consider a more subtle objection leveled against Lewis by philosophers imprint 11 vol. 12, no. 8 (march 2012)

12 John Divers and Joseph Melia. 19 Divers and Melia, in contrast to Lycan and Shalkowski, think that there is nothing modal in any of the materials Lewis uses to define world, or what it is to be true at a world, etc. Rather, they claim that Lewis is unable to give us a complete account of what worlds there are without resorting to primitive modality. Their argument is as follows. They assume that it s possible for there to be alien natural properties. That is, it s possible for there to be perfectly natural properties which are actually uninstantiated, and which can t be built up from actually instantiated properties, in the sense that they are not conjunctive properties with actually instantiated conjuncts, or structural properties with actually instantiated constituents, etc. If this is possible, then Lewis s principle of recombination basically, the priniciple that we can get new worlds by patching together parts of worlds we ve already got doesn t give us a complete account of what worlds there are, since recombining actual materials, or materials obtained by recombining from actual materials, won t generate alien natural properties. (That s basically what alien means.) And so in order to say what worlds there are, we need to invoke more than recombination. Now, it seems that if there could be alien natural properties, there should be no finite bound on the number of possible alien natural properties out there. It seems ad hoc to say there are exactly 17, or a billion, alien natural properties in the multiverse; and so it seems that if we accept the possibility of alien properties in the first place, we should hold that for any finite natural number n, there are at least n alien properties to be found across the space of worlds. But once this is granted, argue Divers and Melia, there is no way to give in non-modal terms a complete account of what worlds there are. For we can t just say that there are infinitely many alien natural properties spread across the worlds; or that for any finite n there is a world where n distinct alien natural properties are instantiated. Why not? Well, to satisfy those tenets there has to be, across the space of worlds, a denumerable sequence of alien natural properties P 1, P 2,, P n. Now, let S be the set of all the worlds that there are. S satisfies both those tenets, of course; but so does the set S* which is the subset of S containing all the members of S except those worlds where, say, P 1 is instantiated. Because with P 1 missing, there are still of course infinitely many alien properties left; so any tenet you laid down to tell you that there were infinitely many alien natural properties out there in the space of worlds won t be able to discriminate between its being P 1, P 2,, P n that exist across the worlds or merely P 2,, P n that exist. And so there is no tenet you can lay down that will completely yield all the worlds that there are unless, of course, we say something like All the possible alien natural properties are instantiated somewhere across the space of worlds. But that only does the job if the possible here is a modal primitive, not to be subjected to the Lewisian analysis (for otherwise this would reduce to the trivial All the alien properties that exist across the worlds exist across the worlds ). And so the only way to completely say what worlds there are is to invoke primitive modality. A couple of attempts have been made at showing that Lewisians can meet the challenge Divers and Melia lay at their door. Bremer (2003) argues that there are additional non-modal tenets available to Lewis that will plug the gap, whereas Paseau (2006) argues that the Divers/Melia argument doesn t in fact show that the tenets considered are incomplete in the sense Divers and Melia claim. I am with Divers and Melia in thinking that these attempts have been unsuccessful and I won t consider any such line of response further. 20 Rather, I will argue that meeting the Divers/Melia demand is simply unnecessary: that while Divers and Melia are right about what the Lewisian realist cannot do, there is no demand that she should be able to do it in the first place. Hence while Divers and Melia are right about the analytic limit of Lewisian realism, this poses no threat to that theory s reductive ambitions. 19. Divers and Melia (2002). 20. Divers and Melia (2003), (2006). philosophers imprint 12 vol. 12, no. 8 (march 2012)